The Finite Element Method FEM

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The Finite Element Method FEM

مُساهمة  haithamtaan في الأربعاء يناير 21, 2009 3:18 am

The Finite Element Method (FEM) has developed into a key indispensable technology in the modelling and simulation of advanced engineering systems in various fields like housing transportation, communications, and so on. In building such advanced engineering
systems, engineers and designers go through a sophisticated process of modelling, simulation, visualization, analysis, designing, prototyping, testing, and lastly, fabrication. Note that much work is involved before the fabrication of the final product or system. This is
to ensure the workability of the finished product, as well as for cost effectiveness. The process is illustrated as a flowchart in Figure 1.1.

This process is often iterative in nature, meaning that some of the procedures are repeated based on the results obtained at a current stage, so as to achieve an optimal performance at the lowest cost for the system to be built. Therefore, techniques related to modelling and simulation in a rapid and effective way play an increasingly important role, resulting in the application of the FEM being multiplied
numerous times because of this.This book deals with topics related mainly to modelling and simulation, which are
underlined in Figure 1.1. Under these topics, we shall address the computational aspects, which are also underlined in Figure 1.1. The focus will be on the techniques of physical, mathematical and computational modelling, and various aspects of computational simulation.
A good understanding of these techniques plays an important role in building an advanced engineering system in a rapid and cost effective way. So what is the FEM? The FEM was first used to solve problems of stress analysis, and has since been applied to many other problems like thermal analysis, fluid flow analysis, piezoelectric analysis, and many others. Basically, the analyst seeks to determine the distribution
of some field variable like the displacement in stress analysis, the temperature or
heat flux in thermal analysis, the electrical charge in electrical analysis, and so on. The FEM is a numerical method seeking an approximated solution of the distribution of field variables in the problem domain that is difficult to obtain analytically. It is done by dividing
the problem domain into several elements, as shown in Figures 1.2 and 1.3. Known physical laws are then applied to each small element, each of which usually has a very simple geometry. Figure 1.4 shows the finite element approximation for a one-dimensional

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تاريخ التسجيل : 19/01/2009

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